Comparative Evaluation of Various Fractal Dimension Estimation Methods

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1、2012EighthInternationalConferenceonSignalImageTechnologyandInternetBasedSystemsComparativeEvaluationofVariousFractalDimensionEstimationMethodsMalhaLehamelKamalHammoucheUniversitéMouloudMammeri,FacultédeGénieUniversitéMouloudMammeri,FacultédeGénieElectrique

2、etd’Informatique,Départementd'Automatique,Electriqueetd’Informatique,Départementd'Automatique,Tizi-ouzou,Algérie.Tizi-ouzou,Algérie.e-mail:lehamelmalha@yahoo.fre-mail:Kamal_hammouche@yahoo.frAbstract—Thefractaldimension(FD)isanindicatorofthedimensionestima

3、tionisintroducedinthenextsection.Incomplexityofform,shapeortextureofimages.Severalfractalsection3,threeapproachesofFDestimationmethodsaredimensionestimationmethodswhichleadtodifferentresultsarepresented.TheresultsofFDestimateusingtheelevenFDdeveloped.Thisp

4、aperdrawsupasurveyonFDestimationestimationmethodsaregiveninsection4.Finally,concludingmethodsandpresentsacomparativeevaluationbetweenelevenremarksaregiveninthelastsection.FDestimationtechniquesbelongingtothreedifferentapproachesnamelybox-counting,areameasu

5、rementandfractionalII.FRACTALDIMENSIONESTIMATIONBrownianmotion.TheconceptoffractalisdefinedbyMandelbrotforaKeywords-Fractaldimensionestimation;imageanalysis;box-mathematicalsetsinwhichtheHausdorff-Besicovichcounting;areameasurement;fractionalBrownianmotion

6、(fBm).dimensionstrictlyexceedsthetopologicaldimension[1].TheHausdorffdimensionofafractalsetisbyI.INTRODUCTIONdefinitionthelimitwhenthediameterofthecoversetgoesFractalgeometryisintroducedbyMandelbrotin1982[1]tozero:inordertocharacterizetheirregularit

7、yandtodescribethe (1)behaviorofthecomplexobjectsinnatureorartificialobjectswhereisdefinedas:thatmaynotbetreatedingeneralbyEuclideangeometry. (2)Thesesetscalledfractalsorfractalobjectsarecharacterizedbyaselfsimila

8、rityproperty.Itimpliesthatthefractalisisa—coverof,i.e.,afinitecollectionofsetsofexactlyorstaticallysimilartothewholeatanymagnificationdiameteratmostthatcovertheset.orreductionlevel.Theformofanobjectisinva